Carefully wash parsley to remove any dirt; dry well and place in a salad bowl. Add Parmesan to the parsley. Add sun-dried tomatoes, along with garlic. Toss well to combine.

Wash basil to remove any sand, then dry well. Place the basil leaves in the bowl of a food processor and add oil, vinegar, and salt and pepper to taste; process until smooth. Stir shallots and garlic into the dressing.

Drizzle dressing over salad and toss well to combine ingredients. Taste and adjust seasonings. Divide among six salad plates, garnish with some shaved Parmesan, and serve.